1. Economic Analysis (cont’d) Last Lecture: Cash Flow Illustrations The Concept of Interest The 5 Variables Equivalence Equations I: Case 1

2. Equivalence Equations I Used when interest rate is… - Compounded and Constant - Compounded and changing a finite number of times

3. Equivalence Equations I Case 2: Description: Finding the initial amount (P) that would yield a future amount (F)at the end of a given period Example: The Studbaker ’55 car currently under repair. Will be ready by 2005, at a price of $30,000. How much should Jim put away now in order to be able to pay for the car in 2005?

4. Equivalence Equations I CASE 2 (cont’d) Problem Definition: This is a Single Payment Present Worth (SPPW) problem Cash Flow Diagram: Computational Formula: 20012005 PF

5. Equivalence Equations I Case 3: Description: Finding the amount of uniform annual payments (A) that would yield a certain future amount (F)at the end of a given period Example: The Studbaker ’55 antique car is currently under repair. Will be ready by 2005, at a price of $30,000. Jim agrees to pay 5 yearly amounts until 2005, starting December 2001. How much should he pay every year?

6. Equivalence Equations I CASE 3 (cont’d) Problem Definition: This is a Uniform Series Sinking Fund Deposit (USSFD) problem Cash Flow Diagram: Computational Formula: 2001 2005 AAAAA F

7. Equivalence Equations I Case 4: Description: Finding the final compounded amount (F) at the end of a given period due to uniform annual payments (A). Example: The Studbaker ’55 antique car is currently under repair, and will be ready by 2005. Jim agrees to pay $5,000 yearly until 2005, starting December 2001. How much will he end up paying for the car by the year 2005?

8. Equivalence Equations I CASE 4 (cont’d) Problem Definition: This is a Uniform Series Compounded Amount (USCA) problem Cash Flow Diagram: Computational Formula: 20012005 F AAAAA

9. Case 5: Description: Finding the initial amount (P) that would yield specified uniform future amounts (A) over a given period. Example: Jim takes the car now. He has enough money to pay for it, but rather decides to pay in annual installments of $4500 over a 5-year period (now till 2005). How much should he set aside now so that he can make such annual payments? Equivalence Equations I

10. CASE 5 (cont’d) Problem Definition: This is a Uniform Series Present Worth (USPW) problem Cash Flow Diagram: Computational Formula: 20012005 P AAAAA

11. Equivalence Equations I Case 6: Description: Finding the amount uniform annual payments (A) over a given period, that would completely recover an initial amount (P). E.g. credit card monthly payments Example: Jim receives a loan of $20,000 from PEFCU to pay for the car now. How much will he have to pay to the bank every year?

12. Equivalence Equations I CASE 6 (cont’d) Problem Definition: This is a Capital Recovery (CR) problem. The bank seeks to recover its capital from Jim. Cash Flow Diagram: Computational Formula: 2001 2005 P AAAAA